Question

Please Help!! :D Find the value of y.

Answer 1

Answer:

$y=2\sqrt{2}$

Step-by-step explanation:

The Pythagorean theorem is a theorem that can be applied to the sides of a right triangle. Please note that a right angle refers to an angle with a measure of (90) degrees. A box around an angle shows that the angle is a right angle, or has a measure of (90) degrees. The Pythagorean theorem states the following,

$a^2+b^2=c^2$

Where (a) and (b) are the legs of the triangle, or the side adjacent to the right angle in the right triangle. (c) is the side opposite the right angle, or the hypotenuse of the triangle. One can apply this theorem to the smallest triangle in the diagram to find (y),

$a^2+b^2=c^2$

Substitute,

$(1)^2+(y)^2=(3)^2$

Simplify,

$(1)^2+(y)^2=(3)^2$

$1+y^2=9$

Inverse operations,

$1+y^2=9$

$y^2=8$

$y=\sqrt{8}$

Take a factor from out of the square root. Remember that a number times itself under the radical is equal to the number. This can be simply stated as the following: ($\sqrt{a*a}=a$),

$y=\sqrt{8}$

$8=2*2*2$

$y=\sqrt{8}$

$y=\sqrt{2*2*2}$

$y=2\sqrt{2}$